Walking of the Quadruped, Biped, etc.—As the earth, because of its solidity, will bear any amount of pressure to which it may be subjected, the size, shape, and weight of animals destined to traverse its surface are matters of little or no consequence. As, moreover, the surface trod upon is rigid or unyielding, the extremities of quadrupeds are, as a rule, terminated by small feet. Fig.18 (contrast with fig.17).

In this there is a double purpose—the limited area presented to the ground affording the animal sufficient support and leverage, and enabling it to disentangle its feet with the utmost facility, it being a condition in rapid terrestrial progression that the points presented to the earth be few in number and limited in extent, as this approximates the feet of animals most closely to the wheel in mechanics, where the surface in contact with the plane of progression is reduced to a minimum. When the surface presented to a dense resisting medium is increased, speed is diminished, as shown in the tardy movements of the mollusc, caterpillar, and slowworm, and also, though not to the same extent, in the serpents, some of which move with considerable celerity. In the gecko and common house-fly, as is well known, the travelling surfaces are furnished with suctorial discs, which enable those creatures to walk, if need be, in an inverted position; and “the tree-frogs (Hyla) have a concave disc at the end of each toe, for climbing and adhering to the bark and leaves of trees. Some toads, on the other hand, are enabled, by peculiar tubercles or projections from the palm or sole, to clamber up old walls.”21 A similar, but more complicated arrangement, is met with in the arms of the cuttle-fish.

The movements of the extremities in land animals vary considerably.

In the kangaroo and jerboa,22 the posterior extremities only are used, the animals advancing per saltum, i.e. by a series of leaps.23

The deer also bounds into the air in its slower movements; in its fastest paces it gallops like the horse, as explained at pp. 40–44. The posterior extremities of the kangaroo are enormously developed as compared with the anterior ones; they are also greatly elongated. The posterior extremities are in excess, likewise, in the horse, rabbit,24 agouti, and guinea pig. As a consequence these animals descend declivities with difficulty. They are best adapted for slightly ascending ground. In the giraffe the anterior extremities are longer and more powerful, comparatively, than the posterior ones, which is just the opposite condition to that found in the kangaroo.

In the giraffe the legs of opposite sides move together and alternate, whereas in most quadrupeds the extremities move diagonally—a remark which holds true also of ourselves in walking and skating, the right leg and left arm advancing together and alternating with the left leg and right arm (fig.19).

In the hexapod insects, according to MÜller, the fore and hind foot of the one side and the middle one of the opposite side move together to make one step, the three corresponding and opposite feet moving together to form the second step. Other and similar combinations are met with in the decapods.

The alternating movements of the extremities are interesting as betokening a certain degree of flexuosity or twisting, either in the trunk or limbs, or partly in the one and partly in the other.

This twisting begets the figure-of-8 movements observed in walking, swimming, and flying. (Compare figs.6, 7, and 26 x, pp. 28 and 55; figs.18 and 19, pp.37 and 39; figs.32 and 50, pp. 68 and 97; figs.71 and 73, p.144; and fig.81, p.157.)

Locomotion of the Horse.—As the limits of the present volume forbid my entering upon a consideration of the movements of all the animals with terrestrial habits, I will describe briefly, and by way of illustration, those of the horse, ostrich, and man. In the horse, as in all quadrupeds endowed with great speed, the bones of the extremities are inclined obliquely towards each other to form angles; the angles diminishing as the speed increases. Thus the angles formed by the bones of the extremities with each other and with the scapulÆ and iliac bones, are less in the horse than in the elephant. For the same reason they are less in the deer than in the horse. In the elephant, where no great speed is required, the limbs are nearly straight, this being the best arrangement for supporting superincumbent weight. The angles formed by the different bones of the wing of the bird are less than in the fleetest quadruped, the movements of wings being more rapid than those of the extremities of quadrupeds and bipeds. These are so many mechanical adaptations to neutralize shock, to increase elasticity, and secure velocity. The paces of the horse are conveniently divided into the walk, the trot, the amble, and the gallop. If the horse begins his walk by raising his near fore foot, the order in which the feet are lifted is as follows:—first the left fore foot, then the right or diagonal hind foot, then the right fore foot, and lastly the left or diagonal hind foot. There is therefore a twisting of the body and spiral overlapping of the extremities of the horse in the act of walking, in all respects analogous to what occurs in other quadrupeds25 and in bipeds (figs.18 and 19, pp.37 and 39). In the slowest walk Mr. Gamgee observes “that three feet are in constant action on the ground, whereas in the free walk in which the hind foot passes the position from which the parallel fore foot moves, there is a fraction of time when only two feet are upon the ground, but the interval is too short for the eye to measure it. The proportion of time, therefore, during which the feet act upon the ground, to that occupied in their removal to new positions, is as three to one in the slow, and a fraction less in the fast walk. In the fast gallop these proportions are as five to three. In all the paces the power of the horse is being exerted mainly upon a fore and hind limb, with the feet implanted in diagonal positions. There is also a constant parallel line of positions kept up by a fore and hind foot, alternating sides in each successive move. These relative positions are renewed and maintained. Thus each fore limb assumes, as it alights, the advanced position parallel with the hind, just released and moving; the hind feet move by turns, in sequence to their diagonal fore, and in priority to their parallel fellows, which following they maintain for nearly half their course, when the fore in its turn is raised and carried to its destined place, the hind alighting midway. All the feet passing over equal distances and keeping the same time, no interference of the one with the other occurs, and each successive hind foot as it is implanted forms a new diagonal with the opposite fore, the latter forming the front of the parallel in one instant, and one of the diagonal positions in the next: while in the case of the hind, they assume the diagonal on alighting and become the terminators of the parallel in the last part of their action.”

In the trot, according to Bishop, the legs move in pairs diagonally. The same leg moves rather oftener during the same period in trotting than in walking, or as six to five. The velocity acquired by moving the legs in pairs, instead of consecutively, depends on the circumstance that in the trot each leg rests on the ground during a short interval, and swings during a long one; whilst in walking each leg swings a short, and rests a long period. The undulations arising from the projection of the trunk in the trot are chiefly in the vertical plane; in the walk they are more in the horizontal.

The gallop has been erroneously believed to consist of a series of bounds or leaps, the two hind legs being on the ground when the two fore legs are in the air, and vice versÂ, there being a period when all four are in the air. Thus Sainbell in his “Essay on the Proportions of Eclipse,” states “that the gallop consists of a repetition of bounds, or leaps, more or less high, and more or less extended in proportion to the strength and lightness of the animal.” A little reflection will show that this definition of the gallop cannot be the correct one. When a horse takes a ditch or fence, he gathers himself together, and by a vigorous effort (particularly of the hind legs), throws himself into the air. This movement requires immense exertion and is short-lived. It is not in the power of any horse to repeat these bounds for more than a few minutes, from which it follows that the gallop, which may be continued for considerable periods, must differ very materially from the leap.

The pace known as the amble is an artificial movement, produced by the cunning of the trainer. It resembles that of the giraffe, where the right fore and right hind foot move together to form one step; the left fore and left hind foot moving together to form the second step. By the rapid repetition of these movements the right and left sides of the body are advanced alternately by a lateral swinging motion, very comfortable for the rider, but anything but graceful. The amble is a defective pace, inasmuch as it interferes with the diagonal movements of the limbs, and impairs the continuity of motion which the twisting, cross movement begets. Similar remarks might be made of the gallop if it consisted (which it does not) of a series of bounds or leaps, as each bound would be succeeded by a halt, or dead point, that could not fail seriously to compromise continuous forward motion. In the gallop, as in the slower movements, the horse has never less than two feet on the ground at any instant of time, no two of the four feet being in exactly the same position.

Mr. Gamgee, who has studied the movements of the horse very carefully, has given diagrams of the walk, trot, and gallop, drawn to a scale of the feet of a two-year-old colt in training, which had been walked, trotted, and galloped over the ground for the purpose. The point he sought to determine was the exact distance through which each foot was carried from the place where it was lifted to that where it alighted. The diagrams are reproduced at figures 21, 22, and 23. In figure 23 I have added a continuous waved line to indicate the alternating movements of the extremities; Mr. Gamgee at the time he wrote26 being, he informs me, unacquainted with the figure-of-8 theory of animal progression as subsequently developed by me. Compare fig.23 with figs.18 and 19, pp.37 and 39; with fig.50, p.97; and with figs.71 and 73, p.144.

In examining figures 21, 22, and 23, the reader will do well to remember that the near fore and hind feet of a horse are the left fore and hind feet; the off fore and hind feet being the right fore and hind feet. The terms near and off are technical expressions, and apply to the left and right sides of the animal. Another point to be attended to in examining the figures in question, is the relation which exists between the fore and hind feet of the near and off sides of the body. In slow walking the near hind foot is planted behind the imprint made by the near fore foot. In rapid walking, on the contrary, the near hind foot is planted from six to twelve or more inches in advance of the imprint made by the near fore foot (fig.21 represents the distance as eleven inches). In the trot the near hind foot is planted from twelve to eighteen or more inches in advance of the imprint made by the near fore foot (fig.22 represents the distance as nineteen inches). In the gallop the near hind foot is planted 100 or more inches in advance of the imprint made by the near fore foot (fig.23 represents the distance as 110 1/2 inches). The distance by which the near hind foot passes the near fore foot in rapid walking, trotting, and galloping, increases in a progressive ratio, and is due in a principal measure to the velocity or momentum acquired by the mass of the horse in rapid motion; the body of the animal carrying forward and planting the limbs at greater relative distances in the trot than in the rapid walk, and in the gallop than in the trot. I have chosen to speak of the near hind and near fore feet, but similar remarks may of course be made of the off hind and off fore feet.

“At fig.23, which represents the gallop, the distance between two successive impressions produced, say by the near fore foot, is eighteen feet one inch and a half. Midway between these two impressions is the mark of the near hind foot, which therefore subdivides the space into nine feet and six-eighths of an inch, but each of these is again subdivided into two halves by the impressions produced by the off fore and off hind feet. It is thus seen that the horse’s body instead of being propelled through the air by bounds or leaps even when going at the highest attainable speed, acts on a system of levers, the mean distance between the points of resistance of which is four feet six inches. The exact length of stride, of course, only applies to that of the particular horse observed, and the rate of speed at which he is going. In the case of any one animal, the greater the speed the longer is the individual stride. In progression, the body moves before a limb is raised from the ground, as is most readily seen when the horse is beginning its slowest action, as in traction.”27

At fig.22, which represents the trot, the stride is ten feet one inch. At fig.21, which represents the walk, it is only five feet five inches. The speed acquired, Mr. Gamgee points out, determines the length of stride; the length of stride being the effect and evidence of speed and not the cause of it. The momentum acquired in the gallop, as already explained, greatly accelerates speed.

“In contemplating length of strides, with reference to the fulcra, allowance has to be made for the length of the feet, which is to be deducted from that of the strides, because the apex, or toe of the horse’s hind foot forms the fulcrum in one instant, and the heel of the fore foot in the next, and vice versÂ. This phenomenon is very obvious in the action of the human foot, and is remarkable also for the range of leverage thus afforded in some of the fleetest quadrupeds, of different species. In the hare, for instance, between the point of its hock and the termination of its extended digits, there is a space of upwards of six inches of extent of leverage and variation of fulcrum, and in the fore limb from the carpus to the toe-nails (whose function in progression is not to be underrated) upwards of three inches of leverage are found, being about ten inches for each lateral biped, and the double of that for the action of all four feet. Viewed in this way the stride is not really so long as would be supposed if merely estimated from the space between the footprints.

“Many interesting remarks might be made on the length of the stride of various animals; the full movement of the greyhound is, for instance, upwards of sixteen feet; that of the hare at least equal; whilst that of the Newfoundland dog is a little over nine feet.”27

Locomotion of the Ostrich.—Birds have been divided by naturalists into eight orders:—the Natatores, or Swimming Birds; the Grallatores, or Wading Birds; the Cursores, or Running Birds; the Scansores, or Climbers; the Rasores, or Scrapers; the ColumbÆ, or Doves; the Passeres; and the Raptores, or Birds of Prey.

The first five orders have been classified according to their habits and modes of progression. The Natatores I shall consider when I come to speak of swimming as a form of locomotion, and as there is nothing in the movements of the wading, scraping, and climbing birds,28 or in the Passeres29 or Raptores, requiring special notice, I shall proceed at once to a consideration of the Cursores, the best examples of which are the ostrich, emu, cassowary, and apteryx.

The ostrich is remarkable for the great length and development of its legs as compared with its wings (fig.24). In this respect it is among birds what the kangaroo is among mammals. The ostrich attains an altitude of from six to eight feet, and is the largest living bird known. Its great height is due to its attenuated neck and legs. The latter are very powerful structures, and greatly resemble in their general conformation the posterior extremities of a thoroughbred horse or one of the larger deer—compare with fig.4, p.21. They are expressly made for speed. Thus the bones of the leg and foot are inclined very obliquely towards each other, the femur being inclined very obliquely to the ilium. As a consequence the angles made by the several bones of the legs are comparatively small; smaller in fact than in either the horse or deer.

The feet of the ostrich, like those of the horse and deer, are reduced to a minimum as regards size; so that they occasion very little friction in the act of walking and running. The foot is composed of two jointed toes,30 which spread out when the weight of the body comes upon them, in such a manner as enables the bird to seize and let go the ground with equal facility. The advantage of such an arrangement in rapid locomotion cannot be over-estimated. The elasticity and flexibility of the foot contribute greatly to the rapidity of movement for which this celebrated bird is famous. The limb of the ostrich, with its large bones placed very obliquely to form a system of powerful levers, is the very embodiment of speed. The foot is quite worthy of the limb, it being in some respects the most admirable structure of its kind in existence. The foot of the ostrich differs considerably from that of all other birds, those of its own family excepted. Thus the under portion of the foot is flat, and specially adapted for acting on plane surfaces, particularly solids.31 The extremities of the toes superiorly are armed with powerful short nails, the tips of which project inferiorly to protect the toes and confer elasticity when the foot is leaving the ground. The foot, like the leg, is remarkable for its great strength. The legs of the ostrich are closely set, another feature of speed.32 The wings of the ostrich are in a very rudimentary condition as compared with the legs.33 All the bones are present, but they are so dwarfed that they are useless as organs of flight. The angles which the bones of the wing make with each other, are still less than the angles made by the bones of the leg. This is just what we would a priori expect, as the velocity with which wings are moved greatly exceeds that with which legs are moved. The bones of the wing of the ostrich are inclined towards each other at nearly right angles. The wings of the ostrich, although useless as flying organs, form important auxiliaries in running. When the ostrich careers along the plain, he spreads out his wings in such a manner that they act as balancers, and so enable him to maintain his equilibrium (fig.25). The wings, because of the angle of inclination which their under surfaces make with the horizon, and the great speed at which the ostrich travels, act like kites, and so elevate and carry forward by a mechanical adaptation a certain proportion of the mass of the bird already in motion. The elevating and propelling power of even diminutive inclined planes is very considerable, when carried along at a high speed in a horizontal direction. The wings, in addition to their elevating and propelling power, contribute by their short, rapid, swinging movements, to continuity of motion in the legs. No bird with large wings can run well. The albatross, for example, walks with difficulty, and the same may be said of the vulture and eagle. What, therefore, appears a defect in the ostrich, is a positive advantage when its habits and mode of locomotion are taken into account.

Professional runners in many cases at matches reduce the length of their anterior extremities by flexing their arms and carrying them on a level with their chest (fig.28, p.62). It would seem that in rapid running there is not time for the arms to oscillate naturally, and that under these circumstances the arms, if allowed to swing about, retard rather than increase the speed. The centre of gravity is well forward in the ostrich, and is regulated by the movements of the head and neck, and the obliquity of the body and legs. In running the neck is stretched, the body inclined forward, and the legs moved alternately and with great rapidity. When the right leg is flexed and elevated, it swings forward pendulum-fashion, and describes a curve whose convexity is directed towards the right side. When the left leg is flexed and elevated, it swings forward and describes a curve whose convexity is directed towards the left side. The curves made by the right and left legs form when united a waved line (vide figs.18, 19, and 20, pp.37, 39, and 41). When the right leg is flexed, elevated, and advanced, it rotates upon the iliac portion of the trunk of the bird, the trunk being supported for the time being by the left leg, which is extended, and in contact with the ground. When the left leg is flexed, elevated, and advanced, it in like manner rotates upon the trunk, supported in this instance by the extended right leg. The leg which is on the ground for the time being supplies the necessary lever, the ground the fulcrum. When the right leg is flexed and elevated, it rotates upon the iliac portion of the trunk in a forward direction, the right foot describing the arc of a circle. When the right leg and foot are extended and fixed on the ground, the trunk rotates upon the right foot in a forward direction to form the arc of a circle, which is the converse of that formed by the right foot. If the arcs alternately supplied by the right foot and trunk are placed in opposition, a more or less perfect circle is produced, and thus it is that the locomotion of animals is approximated to the wheel in mechanics. Similar remarks are to be made of the left foot and trunk. The alternate rolling of the trunk on the extremities, and the extremities on the trunk, utilizes or works up the inertia of the moving mass, and powerfully contributes to continuity and steadiness of action in the moving parts. By advancing the head, neck, and anterior parts of the body, the ostrich inaugurates the rolling movement of the trunk, which is perpetuated by the rolling movements of the legs. The trunk and legs of the ostrich are active and passive by turns. The movements of the trunk and limbs are definitely co-ordinated. But for this reciprocation the action of the several parts implicated would neither be so rapid, certain, nor continuous. The speed of the ostrich exceeds that of every other land animal, a circumstance due to its long, powerful legs and great stride. It can outstrip without difficulty the fleetest horses, and is only captured by being simultaneously assailed from various points, or run down by a succession of hunters on fresh steeds. If the speed of the ostrich, which only measures six or eight feet, is so transcending, what shall we say of the speed of the extinct Æpyornis maximus and Dinornis giganteus, which are supposed to have measured from sixteen to eighteen feet in height? Incredible as it may appear, the ostrich, with its feet reduced to a minimum as regards size, and peculiarly organized for walking and running on solids, can also swim. Mr. Darwin, that most careful of all observers, informs us that ostriches take to the water readily, and not only ford rapid rivers, but also cross from island to island. They swim leisurely, with neck extended, and the greater part of the body submerged.

Locomotion in Man.—The speed attained by man, although considerable, is not remarkable. It depends on a variety of circumstances, such as the height, age, sex, and muscular energy of the individual, the nature of the surface passed over, and the resistance to forward motion due to the presence of air, whether still or moving. A reference to the human skeleton, particularly its inferior extremities, will explain why the speed should be moderate.

On comparing the inferior extremities of man with the legs of birds, or the posterior extremities of quadrupeds, say the horse or deer, we find that the bones composing them are not so obliquely placed with reference to each other, neither are the angles formed by any two bones so acute. Further, we observe that in birds and quadrupeds the tarsal and metatarsal bones are so modified that there is an actual increase in the number of the angles themselves. In the extremities of birds and quadrupeds there are four angles, which may be increased or diminished in the operations of locomotion. Thus, in the quadruped and bird (fig.4, p.21, and fig.24, p. 47), the femur forms with the ilium one angle (a); the tibia and fibula with the femur a second angle (b); the cannon or tarso-metatarsal bone with the tibia and fibula a third angle (c); and the bones of the foot with the cannon or tarso-metatarsal bone a fourth angle (d). In man three angles only are found, marked respectively a, b, and c (figs.26 and 27, pp.55 and 59). The fourth angle (d of figs.4 and 24) is absent. The absence of the fourth angle is due to the fact that in man the tarsal and metatarsal bones are shortened and crushed together; whereas in the quadruped and bird they are elongated and separated.

As the speed of a limb increases in proportion to the number and acuteness of the angles formed by its several bones, it is not difficult to understand why man should not be so swift as the majority of quadrupeds. The increase in the number of angles increases the power which an animal has of shortening and elongating its extremities, and the levers which the extremities form. To increase the length of a lever is to increase its power at one end, and the distance through which it moves at the other; hence the faculty of bounding or leaping possessed in such perfection by many quadrupeds.34 If the wing be considered as a lever, a small degree of motion at its root produces an extensive sweep at its tip. It is thus that the wing is enabled to work up and utilize the thin medium of the air as a buoying medium.

Another drawback to great speed in man is his erect position. Part of the power which should move the limbs is dedicated to supporting the trunk. For the same reason the bones of the legs, instead of being obliquely inclined to each other, as in the quadruped and bird, are arranged in a nearly vertical spiral line. This arrangement increases the angle formed by any two bones, and, as a consequence, decreases the speed of the limbs, as explained. A similar disposition of the bones is found in the anterior extremities of the elephant, where the superincumbent weight is great, and the speed, comparatively speaking, not remarkable. The bones of the human leg are beautifully adapted to sustain the weight of the body and neutralize shock.35 Thus the femur or thigh bone is furnished at its upper extremity with a ball-and-socket joint which unites it to the cup-shaped depression (acetabulum) in the ilium (hip bone). It is supplied with a neck which carries the body or shaft of the bone in an oblique direction from the ilium, the shaft being arched forward and twisted upon itself to form an elongated cylindrical screw. The lower extremity of the femur is furnished with spiral articular surfaces accurately adapted to the upper extremities of the bones of the leg, viz. the tibia and fibula, and to the patella. The bones of the leg (tibia and fibula) are spirally arranged, the screw in this instance being split up. At the ankle the bones of the leg are applied to those of the foot by spiral articular surfaces analogous to those found at the knee-joint. The weight of the trunk is thus thrown on the foot, not in straight lines, but in a series of curves. The foot itself is wonderfully adapted to receive the pressure from above. It consists of a series of small bones (the tarsal, metatarsal, and phalangeal bones), arranged in the form of a double arch; the one arch extending from the heel towards the toes, the other arch across the foot. The foot is so contrived that it is at once firm, elastic, and moveable,—qualities which enable it to sustain pressure from above, and exert pressure from beneath. In walking, the heel first reaches and first leaves the ground. When the heel is elevated the weight of the body falls more and more on the centre of the foot and toes, the latter spreading out36 as in birds, to seize the ground and lever the trunk forward. It is in this movement that the wonderful mechanism of the foot is displayed to most advantage, the multiplicity of joints in the foot all yielding a little to confer that elasticity of step which is so agreeable to behold, and which is one of the characteristics of youth. The foot may be said to roll over the ground in a direction from behind forwards. I have stated that the angles formed by the bones of the human leg are larger than those formed by the bones of the leg of the quadruped and bird. This is especially true of the angle formed by the femur with the ilium, which, because of the upward direction given to the crest of the ilium in man, is so great that it virtually ceases to be an angle.

The bones of the superior extremities in man merit attention from the fact that in walking and running they oscillate in opposite directions, and alternate and keep time with the legs, which oscillate in a similar manner. The arms are articulated at the shoulders by ball-and-socket joints to cup-shaped depressions (glenoid cavities) closely resembling those found at the hip-joints. The bone of the arm (humerus) is carried away from the shoulder by a short neck, as in the thigh-bone (femur). Like the thigh-bone it is twisted upon itself and forms a screw. The inferior extremity of the arm bone is furnished with spiral articular surfaces resembling those found at the knee. The spiral articular surfaces of the arm bone are adapted to similar surfaces existing on the superior extremities of the bones of the forearm, to wit, the radius and ulna. These bones, like the bones of the leg, are spirally disposed with reference to each other, and form a screw consisting of two parts. The bones of the forearm are united to those of the wrist (carpal) and hand (metacarpal and phalangeal) by articular surfaces displaying a greater or less degree of spirality. From this it follows that the superior extremities of man greatly resemble his inferior ones; a fact of considerable importance, as it accounts for the part taken by the superior extremities in locomotion. In man the arms do not touch the ground as in the brutes, but they do not on this account cease to be useful as instruments of progression. If a man walks with a stick in each hand the movements of his extremities exactly resemble those of a quadruped.

The bones of the human extremities (superior and inferior) are seen to advantage in fig.26; and I particularly direct the attention of the reader to the ball-and-socket or universal joints by which the arms are articulated to the shoulders (x, x´), and the legs to the pelvis (a, a´), as a knowledge of these is necessary to a comprehension of the oscillating or pendulum movements of the limbs now to be described. The screw configuration of the limbs is well depicted in the left arm (x) of the present figure. Compare with the wing of the bird, fig.6, and with the anterior extremity of the elephant, fig.7, p.28. But for the ball-and-socket joints, and the spiral nature of the bones and articular surfaces of the extremities, the undulating, sinuous, and more or less continuous movements observable in walking and running, and the twisting, lashing, flail-like movements necessary to swimming and flying, would be impossible.

The leg in the human subject moves by three joints, viz., the hip, knee, and ankle joints. When standing in the erect position, the hip-joint only permits the limb to move forwards, the knee-joint backwards, and the ankle-joint neither backwards nor forwards. When the body or limbs are inclined obliquely, or slightly flexed, the range of motion is increased. The greatest angle made at the knee-joint is equal to the sums of the angles made by the hip and ankle joints when these joints are simultaneously flexed, and when the angle of inclination made by the foot with the ground equals 30°.

From this it follows that the trunk maintains its erect position during the extension and flexion of the limbs. The step in walking was divided by Borelli into two periods, the one corresponding to the time when both limbs are on the ground; the other when only one limb is on the ground. In running, there is a brief period when both limbs are off the ground. In walking, the body is alternately supported by the right and left legs, and advanced by a sinuous movement. Its forward motion is quickened when one leg is on the ground, and slowed when both are on the ground. When the limb (say the right leg) is flexed, elevated, and thrown forward, it returns if left to itself (i.e. if its movements are not interfered with by the voluntary muscles) to the position from which it was moved, viz. the vertical, unless the trunk bearing the limb is inclined in a forward direction at the same time. The limb returns to the vertical position, or position of rest, in virtue of the power exercised by gravity, and from its being hinged at the hip by a ball-and-socket joint, as explained. In this respect the human limb when allowed to oscillate exactly resembles a pendulum,—a fact first ascertained by the brothers Weber. The advantage accruing from this arrangement, as far as muscular energy is concerned, is very great, the muscles doing comparatively little work.37 In beginning to walk, the body and limb which is to take the first step are advanced together. When, however, the body is inclined forwards, a large proportion of the step is performed mechanically by the tendency which the pendulum formed by the leg has to swing forward and regain a vertical position,—an effect produced by the operation of gravity alone. The leg which is advanced swings further forward than is required for the step, and requires to swing back a little before it can be deposited on the ground. The pendulum movement effects all this mechanically. When the limb has swung forward as far as the inclination of the body at the time will permit, it reverses pendulum fashion; the back stroke of the pendulum actually placing the foot upon the ground by a retrograde, descending movement. When the right leg with which we commenced is extended and firmly placed upon the ground, and the trunk has assumed a nearly vertical position, the left leg is flexed, elevated, and the trunk once more bent forward. The forward inclination of the trunk necessitates the swinging forward of the left leg, which, when it has reached the point permitted by the pendulum movement, swings back again to the extent necessary to place it securely upon the ground. These movements are repeated at stated and regular intervals. The retrograde movement of the limb is best seen in slow walking. In fast walking the pendulum movement is somewhat interrupted from the limb being made to touch the ground when it attains a vertical position, and therefore before it has completed its oscillation.38 The swinging forward of the body may be said to inaugurate the movement of walking. The body is slightly bent and inclined forwards at the beginning of each step. It is straightened and raised towards the termination of that act. The movements of the body begin and terminate the steps, and in this manner regulate them. The trunk rises vertically at each step, the head describing a slight curve well seen in the walking of birds. The foot on the ground (say the right foot) elevates the trunk, particularly its right side, and the weight of the trunk, particularly its left side, depresses the left or swinging foot, and assists in placing it on the ground. The trunk and limbs are active and passive by turns. In walking, a spiral wave of motion, most marked in an antero-posterior direction (although also appearing laterally), runs through the spine. This spiral spinal movement is observable in the locomotion of all vertebrates. It is favoured in man by the antero-posterior curves (cervical, dorsal, and lumbar) existing in the human vertebral column. In the effort of walking the trunk and limbs oscillate on the ilio-femoral articulations (hip-joints). The trunk also rotates in a forward direction on the foot which is placed upon the ground for the time being. The rotation begins at the heel and terminates at the toes. So long as the rotation continues, the body rises. When the rotation ceases and one foot is placed flat upon the ground, the body falls. The elevation and rotation of the body in a forward direction enables the foot which is off the ground for the time being to swing forward pendulum fashion; the swinging foot, when it can oscillate no further in a forward direction, reversing its course and retrograding to a slight extent, at which juncture it is deposited on the ground, as explained. The retrogression of the swinging foot is accompanied by a slight retrogression on the part of the body, which tends at this particular instant to regain a vertical position. From this it follows that in slow walking the trunk and the swinging foot advance together through a considerable space, and retire through a smaller space; that when the body is swinging it rotates upon the ilio-femoral articulations (hip-joints) as an axis; and that when the leg is not swinging, but fixed by its foot upon the ground, the trunk rotates upon the foot as an axis. These movements are correlated and complementary in their nature, and are calculated to relieve the muscles of the legs and trunk engaged in locomotion from excessive wear and tear.

Similar movements occur in the arms, which, as has been explained, are articulated to the shoulders by ball-and-socket joints (fig.26, x x´, p.55). The right leg and left arm advance together to make one step, and so of the left leg and right arm. When the right leg advances the right arm retires, and vice versÂ. When the left leg advances the left arm retires, and the converse. There is therefore a complementary swinging of the limbs on each side of the body, the leg swinging always in an opposite direction to the arm on the same side. There is, moreover, a diagonal set of movements, also complementary in character: the right leg and left arm advancing together to form one step; the left leg and right arm advancing together to form the next. The diagonal movements beget a lateral twisting of the trunk and limbs; the oscillation of the trunk upon the limbs or feet, and the oscillation of the feet and limbs upon the trunk, generate a forward wave movement, accompanied by a certain amount of vertical undulation. The diagonal movements of the trunk and extremities are accompanied by a certain degree of lateral curvature; the right leg and left arm, when they advance to make a step, each describing a curve, the convexity of which is directed to the right and left respectively. Similar curves are described by the left leg and right arm in making the second or complementary step. When the curves formed by the right and left legs or the right and left arms are joined, they form waved tracks symmetrically arranged on either side of a given line. The curves formed by the legs and arms intersect at every step, as shown at fig.19, p.39. Similar curves are formed by the quadruped when walking (fig.18, p.37), the fish when swimming (fig.32, p.68), and the bird when flying (figs.73 and 81, pp.144 and 157).

Fig. 27 shows the simultaneous positions of both legs during a step, divided into four groups. The first group (A), 4 to 7, gives the different positions which the legs simultaneously assume while both are on the ground; the second group (B), 8 to 11, shows the various positions of both legs at the time when the posterior leg is elevated from the ground, but behind the supported one; the third group (C), 12 to 14, shows the positions which the legs assume when the swinging leg overtakes the standing one; and the fourth group (D), 1 to 3, the positions during the time when the swinging leg is propelled in advance of the resting one. The letters a, b, and c indicate the angles formed by the bones of the right leg when engaged in making a step. The letters m, n, and o, the positions assumed by the right foot when the trunk is rolling over it. g Shows the rotating forward of the trunk upon the left foot (f) as an axis. h Shows the rotating forward of the left leg and foot upon the trunk (a) as an axis. Compare with fig.4, p. 21; with fig.24, p.47; and with fig.26, p.55.—After Weber.